Prepare the cornbread with the egg and milk according to the package directions for cornbread in an 8- x 8-inch baking dish. Allow to cool and then proceed with the recipe. The cornbread can be prepared a day or two in advance, covered, and stored at room temperature.
Preheat oven to 325 degrees F.
Slice the cornbread and then cut it into 1-inch cubes. Don’t be concerned if some of it crumbles. Cut the slices of bread into 1-inch pieces. You should have 4 to 5 cups each of the cornbread cubes and French bread pieces or 8 to 10 cups total, give or take.
Spread the cornbread (including any crumbles) and bread cubes on a large rimmed baking sheet. Bake 15 minutes, tossing with a spatula after 10 minutes, until lightly toasted (cornbread will be very golden brown and sandwich bread will be toasted and light golden).
Meanwhile, add sausage to a large skillet and place over MEDIUM heat. Cook, stirring to crumble it, and continue to cook until no longer pink. Use a slotted spoon to transfer the sausage to a paper towel lined plate to drain. Pour off any grease from the skillet and wipe it down with a paper towel.
Return the skillet to MEDIUM-LOW heat and add the butter. When melted, add the onion, apples, celery and carrot. Turn the heat up to MEDIUM-HIGH and cook, stirring frequently, for about 7 to 8 minutes or until veggies and apple are fork tender. Don't allow them to brown, you just want them tender (reduce heat, if necessary). Add the garlic and parsley and cook and stir for another 1 to 2 minutes. Add the sage, poultry seasoning, thyme, marjoram, salt and pepper. Mix well to combine. Remove from the heat.
Preheat oven to 350 degrees F and set an oven rack to the center position. Coat a 13- x 9-inch baking dish with nonstick cooking spray and set aside.
Transfer the toasted cornbread and sandwich bread cubes to a large mixing bowl. Spoon the vegetable and apple mixture and the cooked sausage over the bread and mix well. Add the beaten egg and toss lightly to combine. Add 1 cup of chicken broth and toss again, being careful not to break up the cornbread too much. Add additional chicken broth, a little at a time, until you've reached the desired consistency. Stuffing will dry out a little bit as it cooks but you don't want it to be too wet going into the oven. I don't recommend adding more than a total of 1 ½ to 2 cups of broth.
Transfer stuffing to the prepared baking dish and cover with foil. Bake, covered, at 350 degrees F for 30 minutes. Remove the foil and bake for an additional 10 minutes. For a crispier topping, set the oven to BROIL (don’t raise the oven rack) and continue to cook for an additional 2 or 3 minutes or until browned to your liking.